Trigo dilemma

Geometry Level 4

$\left(\sec^{2}10^{\circ}+\tan 10^{\circ}\right)\left(\sec^{2} 50^{\circ} - \tan 50^{\circ}\right)\left(\sec^{2} 70^{\circ}+\tan 70^{\circ}\right)$

The value of the expression above can be represented in the form $$\dfrac{a-\sqrt{b}}{b}$$ where $$a$$ and $$b$$ are positive coprime integers. Find the value of $$a+b^2$$.

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